Leigh A. Johnston1,2, Adel Foda2,
Michael J. Farrell2,3, Gary F. Egan2,3
1School of Engineering & NICTA VRL,
University of Melbourne, Melbourne, VIC, Australia; 2Howard Florey
Institute, Florey Neuroscience Institutes, Melbourne, VIC, Australia; 3Centre
for Neuroscience, University of Melbourne, Melbourne, VIC, Australia
Statistical
analyses of fractional anisotropy images in diffusion MRI studies are
traditionally approached using parametric tests, under Gaussianity
assumptions, or nonparametric resampling techniques. We present an analytic form for the
distribution of FA, both for Gaussian distributed tensor eigenvalues for
which FA follows a transformed doubly noncentral beta distribution, and a
generalisation to arbitrary eigenvalue distributions. These powerful result permits application
of valid inference statistical tests to FA maps in all experimental
conditions.